\relax 
\ifx\hyper@anchor\@undefined
\global \let \oldcontentsline\contentsline
\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global \let \oldnewlabel\newlabel
\gdef \newlabel#1#2{\newlabelxx{#1}#2}
\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\let \contentsline\oldcontentsline
\let \newlabel\oldnewlabel}
\else
\global \let \hyper@last\relax 
\fi

\citation{breuil-conrad-diamond-taylor}
\citation{gross-zagier}
\citation{stevens:stickel}
\citation{stein-watkins:ns}
\citation{MR2135139}
\citation{cremona:alg}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}}
\citation{agst-bsd}
\citation{neronmodels}
\citation{silverman:aec}
\citation{silverman:aec2}
\citation{atkin-lehner}
\citation{manin:parabolic}
\citation{manin:parabolic}
\@writefile{toc}{\contentsline {section}{\numberline {2}Optimal Elliptic Curve Quotients}{2}{section.2}}
\newlabel{sec:elliptic}{{2}{2}{Optimal Elliptic Curve Quotients\relax }{section.2}{}}
\citation{edix:manin}
\citation{katz-mazur}
\citation{maziso}
\citation{abbull}
\citation{abbull}
\citation{edix:thesis}
\newlabel{conjman}{{2.1}{3}{Optimal Elliptic Curve Quotients\relax }{lem.2.1}{}}
\newlabel{edixman}{{2.2}{3}{Optimal Elliptic Curve Quotients\relax }{lem.2.2}{}}
\newlabel{mazman}{{2.3}{3}{Optimal Elliptic Curve Quotients\relax }{lem.2.3}{}}
\newlabel{thmofraynaud}{{2.4}{3}{Optimal Elliptic Curve Quotients\relax }{lem.2.4}{}}
\newlabel{abulman}{{2.5}{3}{Optimal Elliptic Curve Quotients\relax }{lem.2.5}{}}
\newlabel{agell}{{2.7}{3}{Optimal Elliptic Curve Quotients\relax }{lem.2.7}{}}
\citation{shimura:factors}
\citation{diamond-im}
\citation{diamond-im}
\citation{diamond-im}
\citation{diamond-im}
\citation{diamond-im}
\citation{diamond-im}
\@writefile{toc}{\contentsline {section}{\numberline {3}Quotients of arbitrary dimension}{4}{section.3}}
\newlabel{maninmotiv}{{3}{4}{Quotients of arbitrary dimension\relax }{section.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Generalization to quotients of arbitrary dimension}{4}{subsection.3.1}}
\newlabel{sec:genman}{{3.1}{4}{Generalization to quotients of arbitrary dimension\relax }{subsection.3.1}{}}
\newlabel{lem:Hecke-stable}{{3.1}{4}{Generalization to quotients of arbitrary dimension\relax }{lem.3.1}{}}
\citation{gross}
\citation{lang}
\citation{aginv}
\citation{gonz-lario:manin}
\citation{lang}
\citation{agst-bsd}
\citation{agst-bsd}
\citation{gross-zagier}
\citation{mccallum:kolyvaginw}
\citation{gonz-lario:manin}
\newlabel{def:maninconst}{{3.3}{5}{Generalization to quotients of arbitrary dimension\relax }{lem.3.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Motivation: connection with the conjecture of Birch and Swinnerton-Dyer}{5}{subsection.3.2}}
\citation{ces}
\citation{maziso}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Results and a conjecture}{6}{subsection.3.3}}
\newlabel{maninint}{{3.4}{6}{Results and a conjecture\relax }{lem.3.4}{}}
\newlabel{thm:stein}{{3.5}{6}{Results and a conjecture\relax }{lem.3.5}{}}
\citation{diamond-im}
\citation{gonz-lario:manin}
\citation{abbull}
\newlabel{cor:gen_mazur}{{3.7}{7}{Results and a conjecture\relax }{lem.3.7}{}}
\newlabel{rmk:wl}{{3.9}{7}{Results and a conjecture\relax }{lem.3.9}{}}
\newlabel{thm:stein-raynaud}{{3.10}{7}{Results and a conjecture\relax }{lem.3.10}{}}
\citation{FLSSSW}
\citation{kilford}
\citation{joyce}
\newlabel{thm:moddeg}{{3.11}{8}{Results and a conjecture\relax }{lem.3.11}{}}
\newlabel{conjmannew}{{3.12}{8}{Results and a conjecture\relax }{lem.3.12}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Examples of nontrivial Manin constants}{8}{subsection.3.4}}
\newlabel{sec:counter}{{3.4}{8}{Examples of nontrivial Manin constants\relax }{subsection.3.4}{}}
\citation{maziso}
\citation{dera}
\citation{mazur-ribet}
\citation{neronmodels}
\@writefile{toc}{\contentsline {section}{\numberline {4}Proofs of some of the Theorems}{9}{section.4}}
\newlabel{sec:proofs}{{4}{9}{Proofs of some of the Theorems\relax }{section.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Two lemmas}{9}{subsection.4.1}}
\newlabel{sec:keylem}{{4.1}{9}{Two lemmas\relax }{subsection.4.1}{}}
\newlabel{lem:torker}{{4.1}{9}{Two lemmas\relax }{lem.4.1}{}}
\newlabel{eqn:qexp1}{{1}{9}{Two lemmas\relax }{equation.1}{}}
\citation{mazur-ribet}
\newlabel{qandFexp}{{2}{10}{Two lemmas\relax }{equation.2}{}}
\newlabel{lem:keylem}{{4.2}{10}{Two lemmas\relax }{lem.4.2}{}}
\citation{mazur:eisenstein}
\citation{mazur:eisenstein}
\citation{dera}
\citation{dera}
\citation{maziso}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Proof of Theorem\nobreakspace  {}\ref  {thm:stein}}{12}{subsection.4.2}}
\newlabel{thm:proofstein}{{4.2}{12}{Proof of Theorem~\ref {thm:stein}\relax }{subsection.4.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Proof of Theorem\nobreakspace  {}\ref  {thm:moddeg}}{12}{subsection.4.3}}
\newlabel{sec:moddeg}{{4.3}{12}{Proof of Theorem~\ref {thm:moddeg}\relax }{subsection.4.3}{}}
\citation{abbull}
\citation{abbull}
\citation{maziso}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4}Proof of Theorem\nobreakspace  {}\ref  {thm:stein-raynaud}}{13}{subsection.4.4}}
\newlabel{proof:stein-raynaud}{{4.4}{13}{Proof of Theorem~\ref {thm:stein-raynaud}\relax }{subsection.4.4}{}}
\newlabel{eqn:insert_C}{{3}{13}{Proof of Theorem~\ref {thm:stein-raynaud}\relax }{equation.3}{}}
\newlabel{eqn:dualc}{{4}{14}{Proof of Theorem~\ref {thm:stein-raynaud}\relax }{equation.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Appendix by J.\nobreakspace  {}Cremona: Verifying that $c=1$}{14}{section.5}}
\newlabel{sec:appdx}{{5}{14}{Appendix by J.~Cremona: Verifying that $c=1$\relax }{section.5}{}}
\citation{cremona:onlinetables}
\newlabel{thm:cremona60000}{{5.2}{16}{Appendix by J.~Cremona: Verifying that $c=1$\relax }{lem.5.2}{}}
\bibcite{abbull}{AU96}
\bibcite{aginv}{Aga99}
\bibcite{atkin-lehner}{AL70}
\bibcite{agashe-ribet-stein}{ARS}
\bibcite{agst-bsd}{AS05}
\bibcite{neronmodels}{BLR90}
\bibcite{breuil-conrad-diamond-taylor}{BCDT01}
\bibcite{ces}{CES03}
\bibcite{cremona:alg}{Cre97}
\bibcite{cremona:onlinetables}{Cre}
\bibcite{diamond-im}{DI95}
\bibcite{dera}{DR73}
\bibcite{edix:thesis}{Edi89}
\bibcite{edix:manin}{Edi91}
\bibcite{FLSSSW}{FpS{$^{+}$}01}
\bibcite{gonz-lario:manin}{GL01}
\bibcite{gross}{Gro82}
\bibcite{gross-zagier}{GZ86}
\bibcite{joyce}{Joy05}
\bibcite{kilford}{Kil02}
\bibcite{katz-mazur}{KM85}
\bibcite{lang}{Lan91}
\bibcite{manin:parabolic}{Man72}
\bibcite{mazur:eisenstein}{Maz77}
\bibcite{maziso}{Maz78}
\bibcite{mazur-ribet}{MR91}
\bibcite{mccallum:kolyvaginw}{Mc91}
\bibcite{shimura:factors}{Shi73}
\bibcite{shimura:intro}{Shi94}
\bibcite{silverman:aec}{Sil92}
\bibcite{silverman:aec2}{Sil94}
\bibcite{stein-watkins:ns}{SW04}
\bibcite{stevens:stickel}{Ste89}
\bibcite{MR2135139}{Vat05}